Finite Group Databasebeta

← C73×#62589 #32971993

Subgroups — C73×#62589 #32971993

Order 18688.

1702 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3518C211yesmaximal, characteristic
2C73×#3503C211yesmaximal, characteristic, complemented
3C73×#3363C212yesmaximal, complemented
4C73×#3359C212yesmaximal, complemented
5C73×#3329C216yesmaximal, complemented
6C73×#3328C216yesmaximal, complemented
7C73×#3237C213yesmaximal, complemented
8C73×#3218C213yesmaximal, complemented
9C73×#3172C213yesmaximal, complemented
10C73×#3139C213yesmaximal, complemented
11C73×#2971C211yesmaximal, characteristic, complemented
12Q82×C73—21no—
13Q82×C73C2211yescharacteristic
14#557×C73C2212yes—
15#556×C73—23no—
16#556×C73C2213yes—
17#555×C73C2213yes—
18#554×C73—23no—
19D4×Q8×C73C2216yes—
20D4×Q8×C73C2211yescharacteristic
21#548×C73—21no—
22#544×C73—23no—
23#542×C73—23no—
24#533×C73C2213yes—
25#533×C73C2213yes—
26C2×C4⋊Q8×C73C2213yes—
27#529×C73C2213yes—
28#520×C73—21no—
29#519×C73—21no—
30C4×#41×C73C2211yescharacteristic
31#501×C73C2213yes—
32#497×C73C2213yes—
33#491×C73C2216yes—
34#491×C73C2213yes—
35#489×C73C2211yescharacteristic
36#487×C73C2216yes—
37#487×C73C2216yes—
38#485×C73C22112yes—
39#477×C73C2216yes—
40#475×C73C2216yes—
41#470×C73C2216yes—
42#468×C73C2216yes—
43#462×C73C2216yes—
44#461×C73C2216yes—
45#451×C73C2216yes—
46#448×C73C2216yes—
47C8×Q8×C73C2212yes—
48C4×Q16×C73C2216yes—
49C4×SD16×C73C2216yes—
50#436×C73C2216yes—
51#432×C73C2213yes—
52#419×C73C22112yes—
53C4×M16×C73C2213yes—
54C2×#41×C73D411yescharacteristic
55C22×Q8×C73—21no—
56C22×Q8×C73C2316yes—
57C2×Q16×C73C2316yes—
58C2×SD16×C73C2316yes—
59C2×M16×C73C2316yes—
60C4⋊Q8×C73—23no—
61C4⋊Q8×C73—26no—
62C4⋊Q8×C73—23no—
63C4⋊Q8×C73—23no—
64C4⋊Q8×C73C2316yes—
65C4⋊Q8×C73C2313yes—
66C4⋊Q8×C73C2313yes—
67C4⋊Q8×C73C2313yes—
68C4⋊Q8×C73C2311yescharacteristic
69#126×C73—26no—
70#126×C73—23no—
71#125×C73—26no—
72#125×C73—23no—
73#125×C73C2313yes—
74#124×C73—23no—
75#124×C73—26no—
76#124×C73C2311yescharacteristic
77#123×C73—23no—
78C22⋊Q8×C73—23no—
79C22⋊Q8×C73—23no—
80C22⋊Q8×C73—23no—
81C22⋊Q8×C73—23no—
82C22⋊Q8×C73—212no—
83C22⋊Q8×C73C2313yes—
84C22⋊Q8×C73C2316yes—
85#121×C73—23no—
86#121×C73C2313yes—
87C4×Q8×C73—21no—
88C4×Q8×C73—22no—
89C4×Q8×C73—23no—
90C4×Q8×C73—23no—
91C4×Q8×C73—23no—
92C4×Q8×C73—23no—
93C4×Q8×C73D411yescharacteristic
94C4×Q8×C73C2316yes—
95C4×Q8×C73C2313yes—
96C4×Q8×C73C2311yescharacteristic
97C4×D4×C73—26no—
98C4×D4×C73—23no—
99C4×D4×C73D413yes—
100C4×D4×C73C2313yes—
101C4×D4×C73C2313yes—
102#117×C73—23no—
103#117×C73—23no—
104#117×C73—23no—
105#117×C73D413yes—
106#117×C73C2316yes—
107C2×C4⋊C4×C73—23no—
108C2×C4⋊C4×C73—23no—
109C2×C42×C73C2313yes—
110#107×C73C2316yes—
111#106×C73C2316yes—
112C4⋊C8×C73C2316yes—
113#103×C73C2316yes—
114#103×C73C2316yes—
115#103×C73C23112yes—
116#103×C73C23112yes—
117#103×C73C2312yes—
118#102×C73C2312yes—
119C22⋊C8×C73C2316yes—
120#97×C73C2311yescharacteristic
121#97×C73C2313yes—
122C4×C8×C73C2316yes—
123#41×C73—24no—
124C2×Q8×C73—21no—
125C2×Q8×C73—23no—
126C2×Q8×C73—23no—
127C2×Q8×C73—26no—
128C2×Q8×C73—412no—
129C2×Q8×C73—44no—
130C2×Q8×C73C2×D411yescharacteristic
131C2×Q8×C73C2416yes—
132C2×Q8×C73C2411yescharacteristic
133C2×D4×C73—23no—
134C2×D4×C73C2×D413yes—
135C2×D4×C73C2411yescharacteristic
136C22×C4×C73—26no—
137C22×C4×C73—23no—
138C22×C4×C73C2×D413yes—
139C22×C4×C73C2×D413yes—
140C22×C4×C73C2413yes—
141Q16×C73—46no—
142SD16×C73—46no—
143M16×C73—46no—
144C2×C8×C73C2412yes—
145C2×C8×C73C2416yes—
146C4⋊C4×C73—23no—
147C4⋊C4×C73—23no—
148C4⋊C4×C73—26no—
149C4⋊C4×C73—26no—
150C4⋊C4×C73—21no—
151C4⋊C4×C73—23no—
152C4⋊C4×C73—23no—
153C4⋊C4×C73—23no—
154C4⋊C4×C73—23no—
155C4⋊C4×C73—23no—
156C4⋊C4×C73—26no—
157C4⋊C4×C73—26no—
158C4⋊C4×C73—23no—
159C4⋊C4×C73C2×D413yes—
160C4⋊C4×C73C2×D413yes—
161C4⋊C4×C73C2412yes—
162C4⋊C4×C73C2413yes—
163C4⋊C4×C73C2413yes—
164C22⋊C4×C73—26no—
165C22⋊C4×C73—26no—
166C22⋊C4×C73—23no—
167C22⋊C4×C73—23no—
168C22⋊C4×C73—21no—
169C22⋊C4×C73—21no—
170C22⋊C4×C73—23no—
171C22⋊C4×C73C2×D416yes—
172C42×C73—26no—
173C42×C73—23no—
174C42×C73—26no—
175C42×C73C2×D413yes—
176C42×C73C2×D413yes—
177C42×C73C2413yes—
178C42×C73C2411yescharacteristic
179C23×C73—21no—
180C23×C73C22×D413yes—
181Q8×C73—26no—
182Q8×C73—22no—
183Q8×C73—26no—
184Q8×C73—42no—
185Q8×C73—46no—
186Q8×C73—83no—
187Q8×C73—86no—
188Q8×C73#13714yes—
189D4×C73—26no—
190D4×C73—22no—
191D4×C73—83no—
192C2×C4×C73—26no—
193C2×C4×C73—26no—
194C2×C4×C73—21no—
195C2×C4×C73—22no—
196C2×C4×C73—23no—
197C2×C4×C73—23no—
198C2×C4×C73—26no—
199C2×C4×C73—43no—
200C2×C4×C73—46no—
201C2×C4×C73—86no—
202C2×C4×C73C22×D413yes—
203C2×C4×C73C22×D411yescharacteristic
204C2×C4×C73C22×D411yescharacteristic
205C2×C4×C73C22×D413yes—
206C2×C4×C73C22×D413yes—
207C2×C4×C73C2511yescharacteristic
208C8×C73—22no—
209C8×C73—26no—
210C22×C73—23no—
211C22×C73—23no—
212C22×C73—23no—
213C22×C73—41no—
214C22×C73—41no—
215C22×C73—41no—
216C22×C73C23×D411yescharacteristic
217C4×C73—21no—
218C4×C73—23no—
219C4×C73—23no—
220C4×C73—21no—
221C4×C73—43no—
222C4×C73—42no—
223C4×C73—46no—
224C4×C73—41no—
225C4×C73—43no—
226C4×C73C2×#13716yes—
227C4×C73#58512yes—
228#62589C7311yesmaximal, characteristic, direct product factor, Sylow
229C2×C73—43no—
230C2×C73—81no—
231C2×C73#350011yescharacteristic
232C2×C73C22×#13711yescharacteristic
233C2×C73#358611yescharacteristic
234#3518C2×C7311yescharacteristic
235#3503C2×C7311yescharacteristic, complemented
236#3363C2×C7312yescomplemented
237#3359C2×C7312yescomplemented
238#3329C2×C7316yescomplemented
239#3328C2×C7316yescomplemented
240#3237C2×C7313yescomplemented
241#3218C2×C7313yescomplemented
242#3172C2×C7313yescomplemented
243#3139C2×C7313yescomplemented
244#2971C2×C7311yescharacteristic, complemented
245C73#6258911yescharacteristic, direct product factor, Sylow
246Q82—21no—
247Q82C22×C7311yescharacteristic
248#557C22×C7312yes—
249#556—23no—
250#556C22×C7313yes—
251#555C22×C7313yes—
252#554—23no—
253D4×Q8C22×C7316yes—
254D4×Q8C22×C7311yescharacteristic
255#548—21no—
256#544—23no—
257#542—23no—
258#533C22×C7313yes—
259#533C22×C7313yes—
260C2×C4⋊Q8C22×C7313yes—
261#529C22×C7313yes—
262#520—21no—
263#519—21no—
264C4×#41C22×C7311yescharacteristic
265#501C22×C7313yes—
266#497C22×C7313yes—
267#491C22×C7313yes—
268#491C22×C7316yes—
269#489C22×C7311yescharacteristic
270#487C22×C7316yes—
271#487C22×C7316yes—
272#485C22×C73112yes—
273#477C22×C7316yes—
274#475C22×C7316yes—
275#470C22×C7316yes—
276#468C22×C7316yes—
277#462C22×C7316yes—
278#461C22×C7316yes—
279#451C22×C7316yes—
280#448C22×C7316yes—
281C8×Q8C22×C7312yes—
282C4×Q16C22×C7316yes—
283C4×SD16C22×C7316yes—
284#436C22×C7316yes—
285#432C22×C7313yes—
286#419C22×C73112yes—
287C4×M16C22×C7313yes—
288C2×#41D4×C7311yescharacteristic
289C22×Q8—21no—
290C22×Q8C23×C7316yes—
291C2×Q16C23×C7316yes—
292C2×SD16C23×C7316yes—
293C2×M16C23×C7316yes—
294C4⋊Q8—23no—
295C4⋊Q8—26no—
296C4⋊Q8—23no—
297C4⋊Q8—23no—
298C4⋊Q8C23×C7313yes—
299C4⋊Q8C23×C7316yes—
300C4⋊Q8C23×C7311yescharacteristic
301C4⋊Q8C23×C7313yes—
302C4⋊Q8C23×C7313yes—
303#126—26no—
304#126—23no—
305#125—26no—
306#125—23no—
307#125C23×C7313yes—
308#124—23no—
309#124—26no—
310#124C23×C7311yescharacteristic
311#123—23no—
312C22⋊Q8—23no—
313C22⋊Q8—23no—
314C22⋊Q8—23no—
315C22⋊Q8—23no—
316C22⋊Q8—212no—
317C22⋊Q8C23×C7313yes—
318C22⋊Q8C23×C7316yes—
319#121—23no—
320#121C23×C7313yes—
321C4×Q8—21no—
322C4×Q8—22no—
323C4×Q8—23no—
324C4×Q8—23no—
325C4×Q8—23no—
326C4×Q8—23no—
327C4×Q8D4×C7311yescharacteristic
328C4×Q8C23×C7313yes—
329C4×Q8C23×C7316yes—
330C4×Q8C23×C7311yescharacteristic
331C4×D4—26no—
332C4×D4—23no—
333C4×D4D4×C7313yes—
334C4×D4C23×C7313yes—
335C4×D4C23×C7313yes—
336#117—23no—
337#117—23no—
338#117—23no—
339#117D4×C7313yes—
340#117C23×C7316yes—
341C2×C4⋊C4—23no—
342C2×C4⋊C4—23no—
343C2×C42C23×C7313yes—
344#107C23×C7316yes—
345#106C23×C7316yes—
346C4⋊C8C23×C7316yes—
347#103C23×C7316yes—
348#103C23×C7316yes—
349#103C23×C73112yes—
350#103C23×C73112yes—
351#103C23×C7312yes—
352#102C23×C7312yes—
353C22⋊C8C23×C7316yes—
354#97C23×C7311yescharacteristic
355#97C23×C7313yes—
356C4×C8C23×C7316yes—
357#41—24no—
358C2×Q8—21no—
359C2×Q8—23no—
360C2×Q8—23no—
361C2×Q8—26no—
362C2×Q8—412no—
363C2×Q8—44no—
364C2×Q8C2×D4×C7311yescharacteristic
365C2×Q8C24×C7316yes—
366C2×Q8C24×C7311yescharacteristic
367C2×D4—23no—
368C2×D4C2×D4×C7313yes—
369C2×D4C24×C7311yescharacteristic
370C22×C4—26no—
371C22×C4—23no—
372C22×C4C2×D4×C7313yes—
373C22×C4C2×D4×C7313yes—
374C22×C4C24×C7313yes—
375Q16—46no—
376SD16—46no—
377M16—46no—
378C2×C8C24×C7312yes—
379C2×C8C24×C7316yes—
380C4⋊C4—23no—
381C4⋊C4—23no—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—21no—
385C4⋊C4—23no—
386C4⋊C4—23no—
387C4⋊C4—23no—
388C4⋊C4—23no—
389C4⋊C4—23no—
390C4⋊C4—26no—
391C4⋊C4—26no—
392C4⋊C4—23no—
393C4⋊C4C2×D4×C7313yes—
394C4⋊C4C2×D4×C7313yes—
395C4⋊C4C24×C7312yes—
396C4⋊C4C24×C7313yes—
397C4⋊C4C24×C7313yes—
398C22⋊C4—26no—
399C22⋊C4—26no—
400C22⋊C4—23no—
401C22⋊C4—23no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—23no—
405C22⋊C4C2×D4×C7316yes—
406C42—26no—
407C42—23no—
408C42—26no—
409C42C2×D4×C7313yes—
410C42C2×D4×C7313yes—
411C42C24×C7313yes—
412C42C24×C7311yescharacteristic
413C23—21no—
414C23C22×D4×C7313yes—
415Q8—26no—
416Q8—22no—
417Q8—26no—
418Q8—42no—
419Q8—46no—
420Q8—86no—
421Q8—83no—
422Q8#137×C7314yes—
423D4—26no—
424D4—22no—
425D4—83no—
426C2×C4—26no—
427C2×C4—26no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—23no—
431C2×C4—23no—
432C2×C4—26no—
433C2×C4—43no—
434C2×C4—46no—
435C2×C4—86no—
436C2×C4C22×D4×C7313yes—
437C2×C4C22×D4×C7311yescharacteristic
438C2×C4C22×D4×C7311yescharacteristic
439C2×C4C22×D4×C7313yes—
440C2×C4C22×D4×C7313yes—
441C2×C4C25×C7311yescharacteristic
442C8—22no—
443C8—26no—
444C22—23no—
445C22—23no—
446C22—23no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22C23×D4×C7311yescharacteristic
451C4—23no—
452C4—21no—
453C4—21no—
454C4—23no—
455C4—46no—
456C4—41no—
457C4—43no—
458C4—43no—
459C4—42no—
460C4C2×#137×C7316yes—
461C4#585×C7312yes—
462C2—43no—
463C2—81no—
464C2C73×#350011yescharacteristic
465C2C22×#137×C7311yescharacteristic
466C2C73×#358611yescharacteristic
subgroupG/H
center, socleC22×C73C23×D4
commutator, Frattini, cosocleC2×C4C25×C73
prime radicalC73×#3518C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×#41×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#3503C2semidirect
3. C73×#3363C2semidirect
4. C73×#3359C2semidirect
5. C73×#3329C2semidirect
6. C73×#3328C2semidirect
7. C73×#3237C2semidirect
8. C73×#3218C2semidirect
9. C73×#3172C2semidirect
10. C73×#3139C2semidirect
11. C73×#2971C2semidirect
228. #62589C73direct (N × H)
235. #3503C2×C73semidirect
236. #3363C2×C73semidirect
237. #3359C2×C73semidirect
238. #3329C2×C73semidirect
239. #3328C2×C73semidirect
240. #3237C2×C73semidirect
241. #3218C2×C73semidirect
242. #3172C2×C73semidirect
243. #3139C2×C73semidirect
244. #2971C2×C73semidirect
245. C73#62589direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C73×#35182
C73×#35032
C73×#33632
C73×#33592
C73×#33292
C73×#33282
C73×#32372
C73×#32182
C73×#31722
C73×#31392
C73×#29712
#6258973